[Numeracy 209] Re: manipulatives

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awayman1 at kirksville.k12.mo.us awayman1 at kirksville.k12.mo.us
Mon Feb 22 21:48:37 EST 2010


Thank you for the ideas on manipulatives. I am interested also in
the Making Math Real Curriculum. I agree with you about using
concrete to abstract concepts. I would like some examples of the
intermediate levels (semi-concrete and semi-abstract). I also agree
that there are some things (such as multiplication facts) that need
to become automatic. I think that UNDERSTANDING (conceptualizing)
math ideas needs to be the basis for learning to manipulate numbers.
Rote memorization of processes does not give a solid foundation for
building "fluency" in numeracy.

---- Original Message ----
From: mcarro at lmi.net
To: numeracy at nifl.gov
Subject: [Numeracy 206] Re: manipulatives
Date: Mon, 22 Feb 2010 10:56:46 -0800


>Manipulative materials, I think have most value in the early

>grades.... when developing early concepts of place value, addition

>and

>subtraction, etc. I think the 'scanty understanding" of place value

>

>is at the root of many problems adults have with math. Most

>elementary math books, and certainly adult books, seem to devote mere

>

>paragraphs to the topic, although schools seem to be doing better at

>

>this more recently. Usually, I spend a considerable amount of time

>making sure students (even adults) understand this fundamental

>concept (place value) which is needed throughout the math curriculum.

>

>Decimals, exponential notation, powers of ten, etc. are concepts that

>

>build on place value. I use some base ten blocks, stories, and

>things

>like "straw bundles" , toooth picks, money, etc. to establish the

>hook

>for the basic concept. I spend considerable time demonstrating how

>the "decimal system" works, with 10 digits, 0-9 being the only

>symbols

>use to represent quantities. Once we have gone through the decimal

>system, I challenge the students to create values in the binary

>system, using only 2 digits, 0 and 1, and having them generate the

>values according to the same pattern. They usually are successful

>doing so, and I know they get the idea. When we get to "algebra", I

>

>review the basic concrete ideas (using concrete manipulative

>materials

>if necessary) to review what underlies the new learning, and then

>make

>the leap into the abstract. I do this each and every time we begin

>a

>topic where the prior knowledge required can be demonstrated with

>manipulative materials or real life examples.... the idea is to

>proceed from what is known/familiar to what is unknown/unfamiliar.

>When introducing equations in algebra, I start with the expamples of

>

>"real life" concepts , such as area,, perimeter, volume, etc. as

>examples of algebraic equations that serve as "formulas" that apply

>to

>certain types of problems. We can "solve" for any of the missing

>components of the equation. I also talk about "pi" by wrapping a

>string ( equal in length to the diameter) around many different size

>

>circles, such a plates, cups, etc.... noticing that on each occasion,

>

>it is "a little more than 3 times the diameter of the circle, no

>matter its size". I do a lot of "story telling" about the "geeky

>Greeks" and what they noticed about natural occurrences that still

>holds in math and upon which even today's computer scientists still

>build. ( Of course, it was more than the Greeks.... but it cuts to

>the chase without taking up too much diversionary time... the "geek"

>

>part is for an "emotional zap" and may not work with all groups / I

>follow it with: "I am proud to be a geek". You need to know your

>group).

>

>

>For those interested in the Making Math Real Curriculum, the

>curriculum uses manipulative materials extensively in the early

>stages

>of math, (moving from concrete, to semi-concrete, to semi-abstract

>to

>abstract) but by Pre-Algebra, holds that the concepts need to be

>well established and manipulated mentally. The bridge needs to be

>made from concrete to abstract, and some things to "automaticity"

>before algebra.

>

>

>Maureen Carro, MS, ET

>Academic Learning Solutions

>Alamo, CA

>mcarro at lmi.net

>

>

>

>On Feb 19, 2010, at 10:34 AM, Jacqueline Kiefer wrote:

>

>> Susan, I too am interested in what you learn from Making Math Real.

>>

>> I understand what you mean about manipulatives becoming one more

>> layer of confusion. When I used algebra tiles to explain algebra,

>I

>> BOMBED BIG TIME.

>> However, when I used them to explain integers, there were light

>> bulbs coming on all over the classroom. A deck of cards and a game

>

>> of Integer Showdown is also great.

>> Jackie

>>

>> From: numeracy-bounces at nifl.gov [mailto:numeracy-bounces at nifl.gov]

>

>> On Behalf Of Leslie Hunten

>> Sent: Friday, February 19, 2010 7:39 AM

>> To: The Math and Numeracy Discussion List

>> Subject: [Numeracy 198] Re: manipulatives

>>

>> Susan, please do share what you learn from Making Math Real!

>>

>> Leslie

>>

>>

>> On Thu, Feb 18, 2010 at 3:00 PM, Susan Jones <SUJones at parkland.edu>

>

>> wrote:

>> Nobody uses manipulatives here, which I think is a shame.

>>

>> Hard to make the bridge from concrete to abstract without the

>> concrete, though we sometimes can anyway.

>>

>> We do use some visuals -- but not much of that, either.

>>

>> I wish I could say that the folks working with the more basic than

>

>> pre-algebra did, but I'm 99 44/100% sure they don't either. We

>> explain and wish and wonder why students don't connect math to the

>

>> real world...

>>

>> That said, there's not a lot of evidence (either formal research or

>

>> anecdotal) to say manipulatives help... I've seen them be one more

>

>> layer of confusion, if the connection between the concrete to the

>> symbols isn't solidified. One reason I'm really looking forward to

>

>> the Making Math Real overview is that I have a feeling this does

>> that (or at least makes a good effort;)) and would give me the

>tools

>> to try.

>>

>>

>>

>> Susan Jones

>> Academic Development Specialist

>> Center for Academic Success

>> Parkland College

>> Champaign, IL 61821

>> 217-353-2056

>> sujones at parkland.edu

>> Webmastress,

>> http://www.resourceroom.net

>> http://bicyclecu.blogspot.com

>>

>>

>> >>> Jaye Luke <flipfloprun at gmail.com> 2/18/2010 11:52 AM >>>

>> I haven't taught a math class for adult learners...yet:) But I am

>

>> curious

>> 1- Are you using manipulatives?

>> 2- If you are using manipulatives are they specifically for math

>> (cuisenaire

>> rods) or more generalizable (tokens/tiles)?

>> 3- Do you think the manipulatives are beneficial and why?

>>

>>

>> Cheers

>> jaye

>>

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>>

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>

>

>

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Annell Wayman, Director
Kirksville Program
Adult Education and Literacy
1103 S. Cottage Grove
Kirksville, MO 63501
(660) 665-2865-phone
(660) 626-1477-fax
awayman1 at kirksville.k12.mo.us


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